Question

An object is swung in a horizontal circle on a length of string that is 0.93 m long. Its acceleration is 26.36 m/s2. What is the time it takes the object to complete one horizontal circle?
P.S. : I know the answer is 1.18 seconds but I just don’t know how to get there. Can someone explain to me how to do it? Thanks

Answer 1

Answer:

The object takes approximately 1.180 seconds to complete one horizontal circle.  

Explanation:

From statement we know that the object is experimenting an Uniform Circular Motion, in which acceleration ($a$), measured in meters per square second, is entirely centripetal and is expressed as:

$a = \frac{4\pi^{2}\cdot R}{T^{2}}$ (1)

Where:

$T$ - Period of rotation, measured in seconds.

$R$ - Radius of rotation, measured in meters.

If we know that $a = 26.36\,\frac{m}{s^{2}}$ and $R = 0.93\,m$, then the time taken by the object to complete one revolution is:

$T^{2} = \frac{4\pi^{2}\cdot R}{a}$

$T = 2\pi\cdot \sqrt{\frac{R}{a} }$

$T = 2\pi\cdot \sqrt{\frac{0.93\,m}{26.36\,\frac{m}{s^{2}} } }$

$T \approx 1.180\,s$

The object takes approximately 1.180 seconds to complete one horizontal circle.